The AR model is a process model used in the generation of models where outputs are only dependent on previous outputs, in other words no input are used in modeling, i.e. y_{t} = z_{t} + a1y_{t-1} +a2y_{t-2}
The ARX model is used when the input is included such as y_{t} = z_{t} + a1y_{t-1} +a2y_{t-2} + b1u_{t-1} +b2u_{t-2}